Understanding the Optimal Reproduction Timing for Maximum Average S per Plant

This article aims to clarify the statement: 'If this condition holds, total average S per plant will increase if the production of reproductive biomass during a given short time interval takes place at the latest possible time. Since this is true for any F(t) function, it is also true for the optimal F(t). Optimal F(t) is thus a step function, F(t < t*) = 0 and F(t > t*) = 1, under this condition.'

The statement implies that delaying the production of reproductive biomass (e.g., seeds, fruits) until the very end of a specific time period can lead to a higher average value of 'S' per plant. Here, 'S' represents a variable of interest related to plant performance, potentially representing factors like seed number, seed weight, or overall fitness.

The condition mentioned likely refers to a constraint on resource allocation. This means that the plant has a limited amount of resources available to invest in both growth and reproduction. By delaying reproduction, the plant can maximize its growth during the early part of the time interval, potentially allowing for more resources to be allocated to reproductive biomass production later on.

The statement also highlights that this principle applies to any function 'F(t)' that describes the allocation of resources to reproduction over time. This implies that the optimal allocation strategy, denoted by 'F(t)', follows the same principle. The optimal strategy involves a step function, meaning the plant doesn't invest in reproduction (F(t) = 0) before a specific time point 't' and then fully commits to reproduction (F(t) = 1) afterwards.

In simpler terms, the statement suggests that delaying reproduction until the last possible moment within a given time period can maximize plant performance, as measured by 'S'. This strategy is optimal because it allows the plant to maximize growth and resource accumulation before committing to reproduction, leading to a higher overall reproductive output.